Magnetic skyrmions were first observed in a bulk B20 chiral magnet where the unit cell of the crystal lacks inversion symmetry, i. e. it is noncentrosymmetric, due to the Dzyaloshinskii-Moriya interaction (DMI). The breaking of structural inversion symmetry can also be achieved artificially in extremely thin FM layers adjacent to heavy elements, to induce a nonzero DMI. Many skyrmion properties in the DMI-based system are revealed such as the skyrmion diameters simply inversely proportional to the DMI constant. On the contrary, the triangular lattice, providing a simple realization of a high-symmetry system with six equivalent orientations for the helix, is centrosymmetric. In a two-dimensional triangular lattice magnet with the magnetocrystalline anisotropy perpendicular to the film plane, the magnetic frustration can arise from the coexistence of a nearest -neighbor ferromagnetic exchange interaction and a third-neighbor antiferromagnetic exchange interaction. When an external magnetic field is applied parallelly to the anisotropy, the non-coplanar alignments of spins are favored and even the topologically protected magnetic skyrmions also appear. Based on the Monte Carlo simulation, the dependence of magnetic-field-induced magnetic phase transitions in such magnetic frustrated magnets, including the magnetic phase of skyrmion crystals, and the skyrmion diameters on competing exchange interaction and magnetic field is studied. The results indicate that the diameters of magnetic skyrmions strongly depend on the competing exchange interactions and external magnetic field. Like the diameter features of magnetic skyrmions observed in the conventional DMI-based chiral magnets, the external magnetic field can magnetize the skyrmion periphery spins to reduce the skyrmion diameters. However, the enhanced antiferromagnetic exchange interaction can compress the entire skyrmions. In the framework of the spin wave theory and Monte Carlo simulation results, the diameters of magnetic skyrmions in exchange-interaction-frustrated systems are quantified. The skyrmion diameter decreases linearly with the increase of magnetic field for weak antiferromagnetic exchange interaction. With the increase of antiferromagnetic exchange interaction, the decrease of the skyrmion diameter with increasing magnetic field becomes slow, while the strong magnetic fields may rapidly reduce the skyrmion diameter. With the increase of antiferromagnetic exchange interaction, the maximum and median skyrmion diameters decrease to level-off roughly, while the minimum skyrmion diameters show a rapid decrease first and a great fluctuation later. The phenomena are explained through discussing the variations of configurations and magnetic energies of skyrmions. This work demonstrates the adjustability of skyrmion diameter in centrosymmetric frustrated magnet, which not only improves the understanding of origin of skyrmions, but also supports theoretically the development of new generation of skyrmion-based storage and logic devices.